Basic Mathematics for College Students

9.9 Volume 805

Self Check 6

Find the volume of the cone

shown below. Give the exact

answer and an approximation to

the nearest hundredth.

Now TryProblem 49

2 mi

5 mi

Solution

This is the formula for the volume of a cone.

Substitute 4 for r,the radius of the base, and 6 for h,the height.

Evaluate the exponential expression: (4)^2 16.

Multiply:.

Multiply: 2(16) 32. Write the product so that Pis the last factor.

Use a calculator to do the multiplication.

The exact volume of the cone is 32pft^3. To the nearest hundredth, the volume is
100.53 ft^3.

100.5309649

 32 p

1

 2 p(16) 3 (6) 2



1

3

p(16)(6)

V

1

3

p( 4 )^2 ( 6 )

V

1

3

pr^2 h

EXAMPLE (^7) Water Towers How many cubic
feet of water are needed to fill the spherical water tank
shown on the right? Give the exact answer and an
approximation to the nearest tenth.
StrategyWe will substitute 15 for in the formula
and evaluate the right side.
WHYThe variable represents the volume of a sphere.
Solution
This is the formula for the volume of a sphere.
Substitute 15 for r,the radius of the sphere.
Evaluate the exponential expression: (15)^3 3,375.
Multiply: 4(3,375) 13,500.
Divide:. Write the product
so that Pis the last factor.
Use a calculator to do the multiplication.
The tank holds exactly 4,500pft^3 of water. To the nearest tenth, this is 14,137.2 ft^3.

14,137.16694

13,500

4,500p 3 4,500



13,500

3

p



4

3

p (3,375)

V

4

3

p( 15 )^3

V

4

3

pr^3

V

V^43 pr^3

r

Self Check 7

Find the volume of a spherical

water tank with radius 7 meters.

Give the exact answer and an

approximation to the nearest

tenth.

Now TryProblem 53

15 ft

Using Your CALCULATOR Volume of a Silo

A silo is a structure used for storing grain. The silo shown on the right is a

cylinder 50 feet tall topped with a dome in the shape of a hemisphere. To find the

volume of the silo, we add the volume of the cylinder to the volume of the dome.

Multiply and simplify:.

p( 10 )^2 ( 50 ) Substitute 10 for rand 50 for h.

2 p( 10 )^3

3

1

21

4

3 pr

(^32) ^4
6 pr
(^3) ^2 pr^3
pr 3
(^2) h^2 pr
3
3
pr^2 h

1

2

a

4

3

pr^3 b

VolumecylinderVolumedome(Areacylinder’s base)(Heightcylinder)

1

2

(Volumesphere)

10 ft

50 ft

3

1

3

3

7

2

5

 4

13,500